Thursday, July 22, 2010

Today's mountain top finish involved the climbing of 18.4 km of the western side of Tourmalet (see detailed 3D terrain here), from Luz-Saint-Sauvier onwards. The Tourmalet is the queen of all climbs in the Tour de France and the roads here are some of the highest in France. The Henri Degranges prime was won on the summit by none other than the lanky, steely looking Luxembourgian Andy Schleck, but he did not manage to gain any time advantage on the Spanish climber Contador as the latter finished an inch away from him. Andy promised a strong effort today to aim one last time for the yellow jersey before the final time trial. It didn't happen as planned.

How It Happened :

1. At 18.4 to go, the leaders were in one group of some 10 riders. The speed, as reported on Eurosport at 19K to go was some 25 kmph. But this was on a mild gradient before the Tourmalet officially began (we can assume their speed dropped by 2 Kmph when the gradient kicked in) . At this point, they had 3:59 seconds advantage over the chasing pack.

2. When the leaders had 18K to go, the chasing group with the favorites had just passed the 20K to go sign.

3. Time Gap

= Time To Finish (Slower) - Time to Finish (Faster Leaders)

Knowing the time advantage of 3:59s (0.066 h), speed of leaders = 23 kmph, and distances left for each as stated above, speed of the chasing pack at 20K to go is then calculated by :

Speed = 20 / [0.066 + (18/23)] = 23.58 kmph~ 14.7mph

This speed is high as the sections before the foot of the climb were only gradual.

4. When the leaders were at 10.1 K to go, Carlos Barredo from the chasing pack attacks. The time gap to the leaders drop steadily per kilometer.

5. Andy Schleck who is also in the pack chances upon the opportunity to make something happen. With 10K to go he accelerated and passed Barredo. Contador marked Schleck and took his wheel. Both go hand in hand up the climb, eating up into the time advantage of the leaders (by now, their group had also splintered due to several attacks within.

6. The time gap drops rapidly per kilometer after Schleck's attack (see graph below). How rapid is the Contador-Schleck surge? In a matter of 1.6 km, they completely destroyed the advantage of 1:21s enjoyed at the front by Katusha rider Alexandr Kolobnev. He was caught and passed at 8.4K to go in a matter of 28:30s from the start base of the climb.

7. From hereon, Contador and Schleck are the leaders. With 5K to go, they had a 1:15s advantage on the chasers.

8. Alberto tested Andy's legs by giving it a go at 3.8K to go. Andy responded and trivialized the effort but surprisingly, he did not counterattack. Perhaps both may have found that they were at their absolute limits and hence decided to ride to the summit without any further attacks. There was no sprint to the line but the finishing speed as reported on Eurosport was 14.4 kmph, with a margin of 1:30s over the chasing group. Andy gave a hug to Bert on the summit while the latter winked at Andy and patted his face. "You know, we really are the best around here..."

Data & Calculations :

1. Weather : 10 deg C, low visibility with bit of snow in the morning, overcast with a weak wind from the SW, according to Metro News France. Wind can be consequential to the race. Racers like Carlos Sastre know it. However without a CFD analysis or something similarly sophisticated, the wind vectors are hard to predict given the number of switchbacks, trees, spectators & vehicles. A theoretical analysis of its effect on power to weight ratio was given here for perspectives sake. 2. Procedure : Climb profile divided into 18 sections was borrowed from Velopeloton. Grade was extracted for each individual kilometer. Using a mammoth Eurosport footage recorded using 18 GB of hard drive space (phew), the racers were timed on these 18 sections using my stopwatch with an error of +/- 2 sec. Time gaps/advantages and VAM's were also extracted/timed from the footage video. Power to weight ratio was then calculated with Ferrari's formula using VAM, taking into account the grade of each of the 18 sections. An analysis done this fashion, is a bit on the conservative side opposed to one assuming a constant grade and constant ground velocity. From the perspective of drafting, this analysis is a bit on the overestimating side. All in all, the VAM method is between those two. So for Watts/kg, it is good to represent a figure obtained from this method with an error tolerance of +/- 0.2 W/kg.

3. Change of time gap per kilometer : As shown below :

4. Climb Time : Time taken by Contador & Schleck to complete climb was approx. 53 mins 25 seconds for 18.4 kms according to race footage. However, from Horner's power output file, it was determined the he took some 52 minutes 22 seconds to climb which puts the leaders at 50:37. This is the figure I will use (with some caution because this depends on how it was operated on). It is quite challenging to put this into perspective with previous editions of the Tour. Data is lacking and I have had to pour into past Cycling News reports to extract any sort of approx. information. I have put together what I could glean in the following table. Please do review it, correct me, or help me fill in the blanks if you can.

5. Average speed for climb : Av. speed of the duo from calculations (after passing Kolobnev) = 12.62 mph for 8 km. From Eurosport live online, their finishing speed was recorded to be 9 mph.

6. Average power to weight ratio : Prior to getting caught, Kolobnev and his group exhibited approximately 5.5 W/kg +/- 0.2 W/kg. Average for Contador-Schleck was 6.03 W/kg +/- 0.2 W/kg for 8km after passing Kolobnev. See speed and power to weight ratio below :

7. Climbing Rate (VAM/Ascention Speed) : Average VAM or climbing speed (see detailed explanation for climbing rate) after Schleck and Contador overtook Kolobnev was 1696.5 m/hr. The change of VAM with grade is exhibited below for the parties in the Kolobnev group before the catch and the Schleck-Contador breakaway after the leaders were caught.

Power Meter Data

Both Chris Sorensen and Chris Horner put forth hard efforts during the climb. Surprisingly, Horner made it with the group of chasers and he was the best placed Radioshack rider. As and when I see powermeter information about their efforts, it will be appended here for review/comparisons. The trend of releasing powermeter data is limited in that it monitors only a few riders for a limited amount of time/kilometers before they are expended. But it is should be the most objective indicator of performance, while heart rate is the best indicator of effort.

UPDATE : Chris Horner's Power Output file from SRM is shown below. His average power output is 5.65 W/kg for the entire climb. Relates very well to my estimate envelope of 5.5 +/- 0.2 W/kg as stated above. Notice that SRM missed out on publishing this cyclist's HR value. It is absolutely important to know his effort intensity level. Viewing such information without HR is as good as no information.

Seems just about there. 6.15W/kg is what I had from an back of the napkin calculation. Whats really interesting is whether this decrease in performance is due to racing clean. Also there is SRM data from Sorensen's file today and they're boasting that he was pushing 6.6 W/kg for 10 minutes. In the big scheme of things, 10 km out of 53 isn't so so significant. Now if he could hold that for over 30 minutes like the shady riders of the past, I'd have to switch off my TV and go for a vacation.

So is 1700 m/hr good or bad? Although I remember reading on your site at some point (can't find the post) where you wrote that Tom Danielson's record up Mt. Washington was 1739 m /hour.. I've done the climb once and it was a deathwish. The grade was a consistent 10 or 11% all the way.

Really nice work! I almost did a blog post of my own using the what now appears to be inaccurate estimate of 49 minutes from the CyclingNews forum. One thing you left out, perhaps, was the benefit from drafting, which is still quite significant: worth more than 1% of power, anyway (assume 25% of wind resistance power saved 50% of the time for each rider, with around 13% of the power going into wind resistance).

What sort of interpolation scheme did you use on the grade, which was based on samples every 1km?

Anon @ 11:28 pm : What puzzles me slightly about high performances like 6.6+ W/kg at altitude is that the sea level performance must be much higher due to VO2 max increase. From my (limited) analysis and with discussions from folks in Cycling News forums, a 4-8% decrease in power to weight ratio could potentially be seen as altitude increases. The data I have seen so far are only for runners, and not elite level cyclists. Its bit challenging to extract the role of wind and altitude from this post...I was hoping to find something.

An excellent analysis of the queen stage. Thanks for going back through the books and comparing it to the past efforts. It makes for very interesting reading, and it fits with what I am reading on other sites. I'm also looking forward to seeing Sorensen and Horner's SRM data.

Dan : I just revealed what the data told me, nothing more and the calculations are done using Ferrari's formulas. I noted that they could be a bit on the conservative side but we may never know how they compare to the actual values since we'll never get Contador's power output file. :)

I did not make any assumptions about wind or drafting.. if you notice, the graphs reveal the W/kg of Contador and Schleck only after they pass Kolobnev. This is no trickery, rather its how the advantages of the leaders are spelled out on race footage. From Contador and Schleck's perspective, they received little drafting from 10K to go when they passed Kolobnev. The wind was documented to be weak as well but who knows the real story from spectators. The temperatures were very cool. Almost perfect for high speeds. But you cannot discount the accumulated fatigue from all the riding which may explain why Schleck was on his limit and did not counterattack Contador. I can't remember in the recent past when there were cobbles so early in stage 3 and when they had them do the Tourmalet twice from both sides close to the end of the race. This has been a massive Tour.

Last year this time around Sorensen's power to weight ratio at 4 mins of full effort was 6,5 W/kg (415W) on the slopes of Cote d'Araches . Now he can maintain 6.6 W/kg for 10 minutes (417 W) on much higher Tourmalet. This means he brought his weight down too from the reported 64 kgs, along with increasing his threshold. I don't see any effect of altitude on this power to weight ratio either.

You're really at another level with analysis. Thanks for all the great perspectives. This is not a criticism, but I wish you had an index to this website. I've been digging into your archives and finding amazing articles but that's taking a bit of time.

It's the actually Goddet prize at the top of the Tourmalet. The Desgrange prize is at the top of the Galibier in the Alps. Jacques Goddet succeeded Desgrange as chief organiser of Le Tour in 1936 and held the post for half a century. There's large statue of him at the summit pass.

You're a bit incorrect? The Henri Desgranges prime is awarded to the first rider to cross the "highest" point of the Tour de France. This year, it was the Tourmalet. I know Goddet's statue is on top. I'm wondering if Andy grabbed the Goddet prize as well.

On further inspection, it looks as though the Goddet prize was awarded for the first crossing of the Tourmalet in stage 16 and the Desgrange prize for the winner of the Tourmalet summit finish in stage 17.